Cubic
The cubic crystal system is also known as isometric. As the name suggests, crystals in this system are shaped like cubes, with six faces set at 90 degree angles to each other. The three axes of symmetry, called crystallographic axes, are all perpendicular to each other and of equal lengths. An example of a mineral with crystals that fit into this system is halite, otherwise known as salt.
Tetragonal
Crystals in the tetragonal system are shaped like cuboids. This system also has six faces which sit at 90 degrees to each other. The difference between this system and the cubic one is that although the three crystallographic axes are still perpendicular to each other, only two are of the same length. The third is longer, creating the rectangular shape. Zircon is an example of a mineral in this crystal system.
Hexagonal
Crystals in this system are shaped like hexagonal prisms. Because these crystals have six sides, there is an additional axis. Of the four axes, three are the same length, and are at 60 degrees to one another. The vertical axis is longer than the others and at 90 degrees to the shorter ones. This crystal system is further divided into hexagonal and rhombohedral. Emerald is a gemstone with hexagonal crystals.
Orthorhombic
Orthorhombic crystals are irregular in shape. They have six sides and three perpendicular axes, but each axis is a different length to the others. A number of minerals are made of crystals that fit into this system, including topaz, peridot and tanzanite.
Monoclinic
Crystals of the monoclinic system have six sides and three axes. The axes are all of different lengths and two of them, one being the vertical axis, meet at 90 degrees. The third axis is not perpendicular to the other two. Examples of minerals that fit into the monoclinic crystal system are gypsum and feldspar.
Triclinic
The final crystal system is known as triclinic. Crystals in this system have six sides and three axes of symmetry. None of the axes are equal in length and none are perpendicular to either of the others. Turquoise is an example of a gemstone that fits this crystal system.